Problem: Solve for $x$ and $y$ using elimination. ${-2x-3y = -15}$ ${2x+5y = 17}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2x$ and $2x$ cancel out. $2y = 2$ $\dfrac{2y}{{2}} = \dfrac{2}{{2}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {-2x-3y = -15}\thinspace$ to find $x$ ${-2x - 3}{(1)}{= -15}$ $-2x-3 = -15$ $-2x-3{+3} = -15{+3}$ $-2x = -12$ $\dfrac{-2x}{{-2}} = \dfrac{-12}{{-2}}$ ${x = 6}$ You can also plug ${y = 1}$ into $\thinspace {2x+5y = 17}\thinspace$ and get the same answer for $x$ : ${2x + 5}{(1)}{= 17}$ ${x = 6}$